Question

The value of the test statistic for a one-sample t-test for 21 observations is 1.86.

Question 1: The correct R instruction for finding the P-value for a right-tailed test is: A. 1-pt(1.86, 20) B. 1-pt (1.86,21) C. pt(1.86,21) D. pt(1.86, 20)

Question 2: The correct R instruction for finding the P-value for a two-tailed test is: A. pt(1.86,21) B. 2*(1-pt(1.86,21) C. 2*(1-pt(1.86,20) D. 2*(pt(1.86,20)

Answer 1

Given that,

the value of the test statistic for a one sample t-test for 21 observations is 1.86.

That is, sample size (n)= 21

t = 1.86

Q.1) To find P-value for degrees of freedom = n - 1 = 21 -1 = 20

In R software for finding p-vlaue we used,

pt(test statistic , degrees of freedom)

It gives area to the left of the test statistic value.

Therefore we get p-value for right talied test using command,

1 - pt(1.86, 20) = 0.038829

Answer: A) 1 - pt(1.86, 20)

Q.2)

we know p-value for two tailed test is,

2*P(t > test statistic)

Therefore,

P-value = 2 * ( 1 - pt(1.86,20)) = 0.077658

Answer: C) 2 * (1 - pt(1.86, 20))